TY - JOUR

T1 - Local stability analysis of the azimuthal magnetorotational instability of ideal MHD flows

AU - Zou, Rong

AU - Fukumoto, Yasuhide

N1 - Publisher Copyright:
© The Author(s) 2014.

PY - 2014

Y1 - 2014

N2 - A local stability analysis is carried out of axisymmetric rotating flows of a perfectly conducting fluid subjected to an external azimuthal magnetic field Bθ to non-axisymmetric as well as axisymmetric perturbations. We use the Hain-Lüst equation, capable of dealing with perturbations over a wide range of the axial wavenumber k, which supplements the previous results of |k| → ∞ [G. I. Ogilvie and J. E. Pringle, Mon. Not. R. Astron. Soc. 279, 152 (1996)]. When the magnetic field is sufficiently weak, instability occurs for Ro = rΩ′/(2Ω) < Roc with Roc close to zero, with the maximum growth rate given by the Oort A-value |Ro|, where Ω(r) is the angular velocity of the rotating flow as a function only of r, the distance from the axis of symmetry, and the prime designates the derivative in r. As the magnetic field is increased the flow becomes unstable to waves of long axial wavelength for a finite range of Ro around 0 when Rb = r2(Bθ/r)′/(2Bθ) < -1/4 with growth rate proportional to |Bθ|, giving unstable rotating flows under the current-free background magnetic field.

AB - A local stability analysis is carried out of axisymmetric rotating flows of a perfectly conducting fluid subjected to an external azimuthal magnetic field Bθ to non-axisymmetric as well as axisymmetric perturbations. We use the Hain-Lüst equation, capable of dealing with perturbations over a wide range of the axial wavenumber k, which supplements the previous results of |k| → ∞ [G. I. Ogilvie and J. E. Pringle, Mon. Not. R. Astron. Soc. 279, 152 (1996)]. When the magnetic field is sufficiently weak, instability occurs for Ro = rΩ′/(2Ω) < Roc with Roc close to zero, with the maximum growth rate given by the Oort A-value |Ro|, where Ω(r) is the angular velocity of the rotating flow as a function only of r, the distance from the axis of symmetry, and the prime designates the derivative in r. As the magnetic field is increased the flow becomes unstable to waves of long axial wavelength for a finite range of Ro around 0 when Rb = r2(Bθ/r)′/(2Bθ) < -1/4 with growth rate proportional to |Bθ|, giving unstable rotating flows under the current-free background magnetic field.

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U2 - 10.1093/ptep/ptu139

DO - 10.1093/ptep/ptu139

M3 - Article

AN - SCOPUS:84942518221

VL - 2014

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 11

M1 - 113J01

ER -